Abstract
A Bernstein-type improvement of the Bienaymé-Chebyshev inequality is presented for evaluating a general class of noise-perturbed functions. This result can be applied in the course of solving stochastic optimization problems.
Similar content being viewed by others
References
M. A. H. Dempster, ed.,Stochastic Programming, (1980), Academic Press, London-New York.
W. Hoeffding,Probability inequalities for sums of bounded random variables, (1963), J. Amer. Statist. Assoc.58, 13–30.
P. Kall—A. Prékopa eds.,Recent Results in Stochastic Programming, (1980), Lecture Notes in Econom. and Math. Systems179, Springer, Berlin-Heidelberg.
M. Okamoto,Some inequalities relating to the partial sum of binomial probabilities, (1958), Ann. Inst. Statist. Math.,10, 29–35.
J. Pintér,An improved Chebyshev-inequality for function value estimates by Monte Carlo techniques, (1983) (In Hungarian) Alkalmazott Matematikai Lapok,9, 93–104.
B. T. Poljak,Nonlinear programming methods in the presence of noise, (1978), Math. Programming,14, 87–97.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pintér, J. A modified Bernstein-technique for estimating noise-perturbed function values. Calcolo 22, 241–247 (1985). https://doi.org/10.1007/BF02576496
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02576496